How to Integrate Arcsin Functions: Solving the Integral of Arcsin (2x/(1+x^2))

[XJellieBX]

Homework Statement

Evaluate $$\int arcsin (\frac{2x}{1+x^{2}})$$

Homework Equations

$$\int arcsin x = xarcsinx +\sqrt{1-x^{2}} + C$$

The Attempt at a Solution

I'm not sure where to begin, when I try to substitute the term inside the brackets the equation gets even more complicated. Help?

 

[carlodelmundo]

Are you familiar with integration by parts? The relevant equation you stated uses parts by using u = arcsin x and dV = dX.

Do the same procedure with your above integral... though you are correct that it does get messy!

 

[lubuntu]

You can't just substitute into the equation for arcsin x, it doesn't work that way

 

[XJellieBX]

Thank you =)